The invention relates to a curved surface finishing processing device which is equipment for surface processing, in particular to a processing device using flexible shafts and surface processing toolsto finish or smoothen a processed three-dimensional curved surface, belonging to the field of mechanical engineering and aiming at changing the traditional processing way finishing the surface of a plane workpiece by driving the tool by a rigid shaft and providing a solving scheme for the finishing processing of the three-dimensional surface of the workpiece. The curved surface finishing processing device comprises flexible shafts, flexible shaft support mechanisms, the surface processing tools, a support frame, a base and a work table and is characterized in that the flexible shafts (1) areone group or a plurality of groups, each group of flexible shafts (1) are provided with a plurality of the surface processing tools (3), the flexible shafts (1) are arranged on the support frame (4) through a popularity of the flexible shaft support mechanisms (2), and axes of the flexible shafts (1) are passively bent following the surfaces of workpieces (5) to be processed.